Analysis of health indicators of a system

ABSTRACT

A signal from a system, such as a reactive system, that reflects health indicators of the system may be selected. A signal analyzer may extract the health indicators from the signal and conduct a diagnostics of the health of the system based on the health indicators.

BACKGROUND

Downtime of a complex reactive system (or system that responds toexternal events) is often costly due to lost productivity and expensiverepairs. When the reactive system fails, effort is taken to ensure thatthe downtime is minimized. With the goal of minimizing downtime,reactive systems typically produce many logs of operation that containmultitudes of recorded data.

The logs of operation generally record data for any feature of thereactive system that can be monitored. The health of the system canprobably be inferred from the logs of operation. However, a user of thereactive system may be bogged down with the sheer amount of recordeddata and unable to determine the relevance of the data with regard tothe health of the system.

An expert, in contrast, is able to recognize that different types ofdata have different levels of relevance with respect to the health ofthe system. Accordingly, the expert may rely on just a small portion ofthe multitudinous data to make a quick, accurate inference of the healthof the system. Unfortunately, experts are rare, busy and expensive.Therefore, experts are not available to diagnose the health of everyreactive system.

BRIEF DESCRIPTION OF THE DRAWINGS

Non-limiting and non-exhaustive examples or implementations of thesubject disclosure are described with reference to the followingfigures, wherein like reference numerals refer to like parts throughoutthe various views unless otherwise specified.

FIG. 1 is a schematic block diagram of a system that may quickly andaccurately diagnose a health of a reactive system, according to anexample of the subject disclosure.

FIG. 2 is a schematic block diagram of a diagnostic tool that canautomatically diagnose a health status of a remote reactive system,according to an example of the subject disclosure.

FIG. 3 is a schematic block diagram of a diagnostic tool that canautomatically self-diagnose a health status of a reactive system,according to an example of the subject disclosure.

FIG. 4 is a schematic block diagram of a system that extracts healthindicators of a reactive system from a signal to facilitate healthdiagnostics of the reactive system, according to an example of thesubject disclosure.

FIG. 5 is a schematic block diagram of a system that searches a datastore for diagnostic information to facilitate diagnostics of a reactivesystem according to health indicators that are extracted from a signal,according to an example of the subject disclosure.

FIG. 6 is a schematic block diagram of a system that generates an alarmupon diagnosis of a fault in a reactive system based on healthindicators that are extracted from a signal, according to an example ofthe subject disclosure.

FIG. 7 is a schematic block diagram of a system that decomposes a signalinto health indicators for diagnosis of the health of a reactive system,according to an example of the subject disclosure.

FIG. 8 illustrates an example time-domain analysis of a dynamic mirrorsignal from a press system, according to an example of the subjectdisclosure.

FIG. 9 illustrates an example frequency-domain analysis of a dynamicmirror signal from a press system.

FIG. 10 is a schematic process flow diagram of a method for diagnosingerrors in a reactive system, according to an example of the subjectdisclosure.

FIG. 11 is a schematic process flow diagram of a method for decomposinga signal to extract health indicators, according to an example of thesubject disclosure.

FIG. 12 is a schematic process flow diagram of a method for decomposinga signal to extract health indicators utilizing base functions,according to an example of the subject disclosure.

DETAILED DESCRIPTION

In the following description, numerous specific details are set forth toprovide a thorough understanding of the subject disclosure. One skilledin the relevant art will recognize, however, that the examples andimplementations described herein can be practiced without each of thespecific details, or with other methods, components, materials, etc. Inother instances, well-known structures, materials, or operations are notshown or described in detail to avoid obscuring certain aspects.

According to an aspect of the subject disclosure, described herein is adiagnostic tool that provides automated diagnosis of a fault in areactive system. The fault of a signal can be diagnosed through a“critical health indicator,” an “indicator of health,” an “indicator offaulty behavior,” an “indicator of fault,” or the like. The terms areused interchangeably in the specification to generally mean a signalthat provides an indication of the health of a system.

A signal is chosen that reflects critical health indicators of thereactive system. The signal can reflect information from multiplesources, some of which reflect deviations from optimal operation (alsoreferred to as problem-source signals). The problem-source signals canbe mixed into a final signal without source-specific indication. Thesignal also can be initiated by the system (e.g., for maintaining allsubsystems within working ranges). For system-initiated signals, signalspecific information can be logged by the system and stored for futureuse.

The diagnostic tool can find the deviations from optimal operation byremoving the effect of known system initiated actions and decomposingthe remaining signal into its basic components (e.g. based on theproblem-source signal(s)), each reflecting a certain type of deviation.The basic components can each be used as a health indicator.

Based on an analysis of the critical health indicators, the diagnostictool can discover the root cause of the fault. Discovery of the rootcause of the fault leads to better failure prediction and reduceddowntime of the reactive system.

When used herein, the term “health status” refers to a determination ofthe operating status of a reactive system. For example, the healthstatus reflects whether the reactive system is currently experiencing afault, exhibiting signs that it will experience a fault in the future,or operating normally. The term “health of the system” can be usedinterchangeably with “health status” of the system.

In determining the health status, “critical health indicators,”“indicators of faulty behavior,” “indicators of faults” or “indicatorsof health” are analyzed. The critical health indicators are signals,values, or any other output of the reactive system that may lead to adetermination of the health status of the reactive system. The criticalhealth indicators can also be used to determine the root cause of afault. Determining the root cause of a fault may expedite the repair ofthe fault and minimize downtime of the reactive system.

FIG. 1 illustrates a system 100 that automatically diagnoses a health ofa reactive system quickly and accurately. A reactive system is anysystem that reacts to an internal or external event by changing itsactions, outputs, conditions, statuses, or the like. Examples ofreactive systems include, but are not limited to, mechanical systems,electronic systems, and biological systems. An example of a mechanicalreactive system, a printing press, is used as an example; however, thedescription with regard to the printing press applies to other type ofreactive systems.

When a fault occurs in a reactive system, an expert can often focus onthe root cause of the fault quickly and accurately. The quickness andaccuracy of the expert's analysis leads to the assumption that theexpert needs only to inspect a few signals to find the root cause of thefault. System 100 employs the assumption that the expert needs only tovisually inspect a few signals to find the root cause of the fault.Similar to the expert, system 100 discovers the root cause of the faultby an automated inspection of only a few signals.

System 100 can be better than the expert at fully analyzing the signal102 or set of signals. An expert may be limited with regard to a fullanalysis of the signal 102 or set of signals. For example, frequentlythe strongest anomalous feature in the signal masks other weaker effectsand prevents identification of the weaker effects both by inspection andfeature detection unless the strong effect is removed. The practice ofexperts in this situation is to fix the strong effect and thenre-acquire the signal to look for remaining problems. Accordingly, theexpert troubleshooting procedure is often inefficient. System 100,however, may not suffer from this inefficiency since the weak effectscan often also be seen through signal analysis.

System 100 recognizes that the reactive system generates a signal 102 orset of signals that reflect many critical health indicators for thereactive system. Similar to an electrocardiogram (ECG) signal that isused to diagnose the health of a person, the signal 102 (or set ofsignals) is used to diagnose the health status of the reactive system.The signal 102 or set of signals can be referred to as the ECG of thereactive system or the heartbeat of the reactive system.

The ECG of the reactive system reflects many of the critical healthindicators of the reactive system. With regard to a printing press, theECG of the reactive system is found in a single signal: the dynamicmirror signal. However, an ECG of other types of reactive systems caninclude any number of signals that reflect the critical healthindicators.

System 100 includes a signal selector 104. The signal selector 104selects the signal 102 or set of signals that correspond to the ECG ofthe reactive system. The signal selector 104 receives a plurality ofsignals from the reactive system and selects the signal 102 or set ofsignals that correspond to the ECG of the reactive system from theplurality of signals for further processing.

Upon selection by the signal selector 104, the signal 102 (or set ofsignals) is sent to the signal analyzer 106. The signal analyzer 106automatically performs an analysis of the signal 104 that is similar toconventional automatic ECG analyses. In conventional ECG analysis, knownindicators of faulty behavior are extracted from a pre-defined signal.The indicators of faulty behavior can facilitate diagnoses of healthproblems in humans. Similarly, the signal analyzer 106 facilitates theextraction of the critical health indicators from the signal 102 or setof signals. The critical health indicators facilitate diagnoses of theroot cause of health problems in the reactive system.

Referring now to FIG. 2, illustrated is a system 200 that facilitatesdiagnoses of health problems of a reactive system at a remote location.The diagnosis can occur during operation of the reactive system todetect faults, potential faults, or the like. The diagnosis can alsooccur before or during a development stage of the reactive system toensure that there are no critical design faults.

The system 100 of FIG. 1 is included in a diagnostic tool 202. Thediagnostic tool 202 is a stand-alone tool that is located remote fromthe reactive system. The diagnostic tool 202 has a processor (processor204) that facilitates execution of the signal selector 104, the signalanalyzer 106, and/or any additional components. The signal selector 104,the signal analyzer, and/or any additional components aremachine-executable (e.g., computer-executable) components that arestored in one or more memory locations (memory 206) of the diagnostictool 202.

Processor 204 can be any type of hardware device within a computingsystem that can carry out the instructions of a computer program byperforming operations. Examples of hardware devices include, but are notlimited to, a circuit board, an integrated circuit, any other type ofmicroprocessor, or the like.

Memory 206 can be any type of hardware device or media that can storecomputer executable instructions. Example media that can act as memoryinclude, but are not limited to: random access memory (RAM), read onlymemory (ROM), a hard drive, as well as removable memory devices, whichcan include memory sticks, memory cards, flash drives, external harddrives, and so on.

FIG. 3 shows a reactive system 300 with an embedded diagnostic tool 202.The embedded diagnostic tool 202 facilitates self-diagnosis of healthproblems of the reactive system 300. The self-diagnosis is automatic,based an analysis of the signal 102 or set of signals that contain manyof the critical health indicators of the reactive system 300. Theself-diagnosis can occur during operation of the reactive system todetect faults, potential faults, or the like. The self-diagnosis canalso occur or during a development stage of the reactive system 300 toensure that there are no critical design faults.

The following systems as illustrated in FIGS. 4-7 can be implemented inthe diagnostic tool 202 of FIG. 2 or FIG. 3. The components of FIGS. 4-7are stored in memory location (memory 206) of the diagnostic tool. Theprocessor (processor 204) facilitates execution of the components ofFIGS. 4-7.

The analysis of the signal 102 is performed by the signal analyzer 106.The signal analyzer 106 assumes that the observed health-related signalS′ is a linear combination of multiple problem-specific reactive signalsS_(k), possibly some additional command signals C_(m), and somebackground noise. Each of the signals S_(k) is assumed to be related toa single cause of system performance/health problem.

For example S₁, S₂ could correspond to two vibration-modes havingdifferent frequencies, while S₃ could correspond to mean-velocity drift,and S₄, S₅ could correspond to mechanical shocks at different points intime (e.g. when paper is loaded and when it is emitted). While S_(k)reflects directly the deviation of system components from optimalbehavior, C_(m) reflects system initiated signals (e.g. for keepingcomponents in range).

There may be a set of problem-specific families that are likely to occurin conjunction with various types of problems. In the example above,vibration modes, drift, and shocks may be such a problem-specificfamily. An expert with respect to the reactive system may provide suchproblem-specific sets.

First, the principally known command signals (C_(m)) are eliminated(C_(m): S=S′−Σ_(m)C_(m)).

Then, S is decomposed to find all S_(k)'s.

Traditionally, the detection of such signals is considered for the caseof a single signal-family (e.g., Fourier-analysis for vibrations).Mathematically, such a single signal family corresponds to a “completeorthonormal basis” such that any signal can be completely represented bya linear combination of the basis-signals (frequencies in the case ofFourier analysis), and the basis signals B_(n) are normalized orthogonalto each other, such that the inner-products B_(n)·B_(m) are all zeroexcept when m=n, where they are equal to 1. For two signals, theinner-product is the sum of their point-wise product values. Any signalS is decomposed in any orthonormal basis B as S=Σ_(n)s_(n)B_(n) whereB_(n) is the n^(th) basis signal. The amplitude of component B_(n) isobtained by a simple inner-product operation s_(n)=S·B_(n). Each term inthe linear decomposition above, S_(n)=s_(n)B_(n)≡S↓B_(n) is referred toas the “orthogonal projection” of S onto B_(n), so that the signal S isexpressed as a sum of its orthogonal projections on all the basissignals. The detection of problems in this classical process is done bylooking for components with amplitudes s_(n) above some threshold thatcorresponds to normal operation conditions. In thisorthogonal-projection based framework, signals that do not correlate toa pure basis function have non-zero amplitudes in many or all basissignals and are considered as a noise source regarding the detection ofproblems corresponding to the basis B (e.g., a series of spikesconstitutes noise with regards to detection of vibrations with certainfrequencies). If the amplitude of a basis component is low but the noiselevel in that component due to some other mechanism is higher than apreset threshold or higher than the amplitude of other basis components,the analyzer may falsely declare a problem in that component. Such isthe case, for example, with Frequency analysis of the raw dynamic-mirrorsignal before removing the velocity drift component. The velocity driftcontaminates the lower part of the spectrum and gives rise to highamplitudes for low frequency basis signals—making it hard to detect truelow-frequency problematic vibrations, or giving rise to excessive falsealarms for low-frequency vibrations.

The signal analyzer 106 provides a way to overcome such problemdetection inefficiencies by considering multiple signal-familiestogether as an over-complete basis (i.e. there are multiple ways toexpress each given signal as a linear combination of basis signals).Over-complete bases are no longer orthogonal in the sense that basissignals belonging to different orthogonal families are not orthogonalbetween them-selves. While there is classical prior works onnon-orthogonal (oblique) decomposition in over-complete bases, theyconsider linear oblique projections using a standard technique of“singular value decomposition” SVD. Unfortunately the linear obliqueprojection methods are known to be less stable than orthogonalprojections and enhance noise, since they tend to enhance componentsacross all basis types in a single inseparable step. In particular,linear oblique projections are not suitable for discovering weak problemsignals riding on stronger problem-signals, since other random weaksignals corresponding to noise would be enhanced too and the detectionof the weak-problem signal would have high error rates.

The analysis method yielding a non-linear and stable (noise relisient)approximation of oblique projection onto an over-complete problem-signalbasis, so the advantages of signal decomposition are retained byover-complete signal basis, while avoiding the pitfalls of linearoblique projections. The analysis method is based on two majorprinciples. The first principle is to break the decomposition operationinto an iterative process such that each step involves an orthogonalprojection onto one the signal-families combined with detection andremoval of projected components stronger than the noise level, andpassing the residual signal to the next step.

The second principle is to carefully choose the order of thesignal-families to process, such that stronger components are likely todetected and removed first. The selection of the projection-order couldbe done by the system-expert in case there is a clear ordering of theproblem signal strength for different problem-signal families.Alternatively the order could be found automatically and adaptively foreach new signal by trying orthogonal projection onto each of theproblem-signal families and choosing the projection with largest signalenergy above the background noise level or largest signal to noiseratio.

The analysis method does rely on some reasonable assumptions that thecorrelation between different problem-signal families is relativelylow—i.e. that the magnitude of inner products between basis-signals fromdifferent families is much smaller than 1. This assumption correspondsto the reasonable assumption that an expert would be able todifferentiate between signals characteristic to different problem-typesby their shapes. If the measured signals look the same for differenttypes of problems, they would not be identified separately even by ahuman expert. In practice in the type of problem signal familiesdescribed herein, the magnitude of between-family inner-products is lessthan 0.35 and most are smaller than 0.1 which is consistent with theassumption.

This method provides a good and stable approximation to obliqueprojection. Assume that signal S is composed of two mainproblems—signals corresponding to two different problem types s_(1n),s_(2k), such that the amplitude of the second one is considerablysmaller than the first. In addition the signal contains a multitude ofnoise components V_(j) that are not related to these two problems, butthat have a small inner-product with s_(1n), s_(2k) amplitude in any ofthe bases s₁ or s₂. Hence the example signal can be expressed as:

S=a _(1n) s _(1n) +a _(2k) s _(2k)+Σ_(j>2) V _(j) (where s _(1n) ·V_(j)=C_(1j) , s _(2k) ·V _(j)=C_(2j) such that C _(1j) , C _(2j) <<a_(2k) <<a _(n)).

In the first step of an algorithm that can facilitate the analysismethod, an orthogonal projection of S is applied onto the largercomponent, s_(1n).

A _(1n) =S↓B ₁ =S↓s _(1n) =a _(1n) +a _(2k) c ₁₂+Σ_(j>2) C _(1j).

Where c₁₂ is the inner-product of the non-orthogonal basis unit vectorsc₁₂≡s_(1n)·s_(2k).

A_(1n) can be taken as an approximation of the true amplitude (fordetection purposes). The corresponding relative-approximation errorcontains two terms, one corresponding to the relation between the twosignal components, and the second corresponding to the relation betweenthe noise components and the first signal:

δ_(1n)=(A _(1n) −a _(1n))/a _(1n) =c ₁₂ ·a _(2k) /a _(1n)+Σ_(j>2) C_(1j) /a _(1n).

Based on the assumptions above, the first term is much smaller than 1,due to approximate orthogonality (c₁₂<<1) and the majorness of a_(1n)(a_(2k)/a_(1n)<1). As for the second term corresponding to the noise,one cannot provide an absolute upper limit without additional knowledgeabout the noise. However if the noise components are uncorrelatedbetween themselves or with the signal a_(1n), then the energy of thesecond term is guaranteed to be smaller than the energy of the originalnoise (before projection). An important property here is that therelative error due to the second signal is very small, and the noise isnot enhanced like in linear oblique projection.

In the next step, the signal component s_(in) is declared as detected if|A_(1n)| is larger than some threshold T corresponding to the expectednoise level E{V_(j) ²}^(□). If detection is positive, the projectionS_(1n)=A_(1n)s_(1n) is removed from the measured signal, leaving theresidualR₁=S−A_(1n)s_(1n)=a_(2k)(s_(2k)−c₁₂s_(1n))+Σ_(j>2)[V_(j)⊥s_(1n)] (where[V_(j)⊥s_(1n)]=V_(j)−C_(1j)s_(1n) are the noise components orthogonal tothe basis signal s_(1n)).

Note that the residual R₁ does not depend on a_(1n) (the real magnitudeof the signal component s_(1n)). This feature is used to obtain anapproximation of the magnitude of the component s_(2k) that does dependon the magnitude of the larger component a_(1n). To do this, theresidual R₁ is projected onto s_(2k):

i A_(2k) =R ₁ ↓s _(2k) =a _(2k) −a _(2k) c ₁₂ ²+Σ_(j>2)[V_(j) ⊥s _(1n)]·s _(2k) =a _(2k)(1−c ₁₂ ²)+Σ_(j>2) [C _(2j) −C _(1j) C ₁₂]

In particular, the relative approximation error for a_(2k):

δ_(2k)=(A _(2k) −a _(2k))/_(2k) =c ₁₂ ²+Σ_(j>2)Σ_(j>2) [C _(2j) −C _(1j)c ₁₂ ]/a _(2k).

The part of the relative approximation error due to non-orthogonally ofthe two signal components due c₁₂ ², is much smaller than 1 according tothe assumption above (maximum of ˜0.1, and usually 0.01 or less). Thesecond term in the relative approximation error corresponds to theprojection of the noise component that is orthogonal to s_(1n) and alongs_(2k). The noise energy is again smaller than the original noiseenergy—unlike the noise enhancement effect of linear-oblique projection.Similar to the detection step above, the component s_(2k) is declared asdetected if |A_(2k)| is larger than the noise threshold T.

It should be clear that if there are more signal components with weakermagnitudes, then eventually those components that have energy comparableto or weaker than the noise would not be detected. Yet the detection ofthose signal components above the noise level would not suffer from themixing with other signals that are slightly non-orthogonal even if theirenergy is larger, as long as the stronger signal components are detectedand removed first.

Illustrated in FIG. 4 is a system 400 that extracts critical healthindicators of a reactive system from a signal to facilitate diagnoses ofthe health of the reactive system. System 400 includes a signal selector104 that selects a signal 102 or set of signals that contain many of thecritical health indicators of the reactive system. The signal 102 (orset of signals) is sent to a signal analyzer 106.

The signal analyzer 106 includes an extraction module 402 thatfacilitates extraction of the critical health indicators 404 from thesignal 102 or set of signals. Based on the critical health indicators404, the system analyzer 106 employs a diagnostic module 406 to diagnosea health status of the reactive system. The diagnosis provides a goodsnapshot of the reactive system.

The signal analyzer 106 uses prior knowledge of an expert that a signal102 or set of signals reflects many of the critical health indicators404 of the reactive system to automatically diagnose 406 the healthstatus of the reactive system. The signal analyzer 106 enables anon-expert to quickly and accurately solve complex diagnostic problemsof the reactive system, reducing the downtime of the reactive system andthe costs of incorrect diagnoses. Signal analyzer 106 provides automaticdiagnoses 406 of the root cause of any faults, which reduces the needfor rare, busy, and expensive experts.

Referring now to FIG. 5, illustrated is a system 500 that searches adata store 502 for diagnostic information to facilitate a diagnosis of areactive system according to critical health indicators 404 that areextracted from a signal 102 or set of signals. Data store 502 is aknowledge base of different faults for the reactive system, such thatdata store 502 includes a list of known faults and their correspondingsymptoms. The symptoms correspond to different critical healthindicators 404.

Data store 502 is generally any type of data repository that can storedata in a schema or plurality of schemas and also includes any datarepository that can store flat data without a schema. Data store 502 canalso refer to any type of “memory” device.

System 500 allows an expert's knowledge base to be used by a non-expertwithout the need for actually engaging the expert. The data store 502corresponds to a knowledge base of an expert. In one example, an expertmay populate the data store 502 with the known faults and correspondingsymptoms.

In another example, faults and corresponding system can be determinedthrough machine learning technologies and the data store 502 can bepopulated with the information automatically or after review by anexpert. For example, when new faults are diagnosed and/or differentcorresponding symptoms are identified, the system 500 learns of thediagnosis and/or identification and adds the new fault and/or symptom tothe data store 502. The data store 502 can learn of the diagnosis and/oridentification and add the new fault and/or symptom to the data store502 automatically. The data store 502 can also be populated with the newfault and/or symptom manually (for example, through periodic updatesfrom an expert).

FIG. 6 illustrates a system 600 that alerts a user of a potential healthproblem in a reactive system. The system 600 generates an alarm 604through a generation module 602 upon the diagnosis of a fault in thereactive system. The alarm 604 can also be generated through thegeneration module 602 upon detection of a trend in critical healthindicators 404 that are extracted from a signal 102 or a set of signalsthat indicates a potential future fault. When an alarm 604 is generatedby the generation module 602 upon detection of a suspicious pattern inthe indicators 404, proactive preventative actions can be taken beforethe fault occurs, reducing downtime and associated costs.

FIG. 7 illustrates a system 700 that automatically diagnoses the healthstatus of a reactive system. System 700 includes a signal analyzer 106that decomposes through a decomposition module 702 a signal 102 or setof signals into critical health indicators 404. The signal analyzer 106can diagnose a health status of the reactive system based on thecritical health indicators 404. The signal analyzer 106 can consult adata store 502 to find a fault condition that corresponds to thecritical health indicators 404 or symptoms. System 700 allows bothexperts and non-experts alike to monitor and correct the reactivesystem.

The signal analyzer 106 assumes the critical health indicators 404 forthe reactive system add linearly to form the signal 102 or set ofsignals. In other words, signal 102 (or the set of signals) is assumedto be a decomposition of basic signals that refer to the critical healthindicators 404. Since the critical health indicators 404 add linearly,the signal 102 or set of signals can be additively decomposed.

By clever selection of base functions (e.g., through the base functionselector 704), the decomposition can be performed in a way such that allfault sources of the system can be detected through the critical healthindicators 404. To perform the decomposition, an over complete basis ischosen so that the base functions enhance known fault causes. The choiceof base functions enhances the root causes of the faults and facilitatesautomatic detection of the root causes.

The base functions can be predefined for different signals 102 fromdifferent reactive systems according to an expert's knowledge. Basefunctions can also be derived from the signal 102 or set of signals. Forexample, base functions can be derived from the signal 102 or set ofsignals by applying sparse representation techniques.

The effectiveness of system 700 is exemplified by testing with aHewlett-Packard Company® (HP) Indigo press. Experts have identified onesignal 102 that contains the critical health indicators 404 of mainmechanical and electronic components of the Indigo press: the correctioncommand signal to the dynamic mirror (or dynamic mirror signal).

In the Indigo system, the dynamic mirror is part of the wiring head thatcreates the image on the photo imaging plate (PIP). The dynamic mirrorshifts laser beams with or against the process rotation direction inorder to compensate for changes in speed and angular position of the PIPdue to mechanical and electrical imperfections.

In an ideal press, the angular position of the PIP should follow asmooth, linearly increasing line (modulo 360 degrees), with a slopedepending on the nominal angular speed of the system. In such a system,the dynamic mirror correction command would be a constant signal with nocorrection. However, for an actual press there are often discrepanciesfrom this ideal situation. Dynamic mirror compensations are used tocorrect for the discrepancies.

The dynamic mirror compensates for cumulative effects contributing todeviations in PIP velocity. When the press behaves properly, the dynamicmirror corrects for small deviations. When faults occur, the dynamicmirror corrects for larger deviations, possibly going out of themirror's range. Because the dynamic mirror compensates for cumulativeeffects contributing to PIP velocity deviations, the correction commandsignal reflects all of the cumulative effects.

The signal is pre-processed to remove the command signals or signalsfrom system components as described above. It is assumed that allfactors of the pre-processed signal that contribute to the error addlinearly. Therefore, a linear decomposition can be performed (e.g., by asignal analyzer 106 with a decomposition module 702) on the correctioncommand signal. The linear decomposition is performed in a clever way,facilitating detection of all of the fault sources using one measurementso that all of the fault sources can be addressed at once.

To perform the decomposition, an over complete basis with base functionsthat enhance the known fault causes is employed (e.g., selected by thebase function selector 704). FIG. 8 illustrates an example analysis(that can be performed, for example, by signal analyzer 106) of thecorrection command signal (or dynamic mirror signal) that can beselected by signal selector 104 as the signal 102 for which the analysisis based.

In FIG. 8A, a portion of the raw dynamic mirror signal taken from a HPIndigo 5000 press is plotted. This signal can correspond to signal 102.The x-axis is the time converted to degrees. 360 degrees refers to afull revolution of the blanket drum and corresponds to a singleseparation.

FIG. 8B corresponds to printing a full 4-separation page. Periodic jumpsin the signal (dynamic mirror signal, corresponding to signal 102) areclearly seen (marked by circles for emphasis). The jumps indicate thedisplacement correction commands: every separation in the mirrorcorrects for large displacement deviations of the PIP so as to keep themirror displacement within bounds. These deviations are caused bydeviations of the mean angular velocity of the PIP from the nominalvelocity.

FIG. 8C shows the raw signal after the removal of velocity corrections.Here, the velocity deviation is apparent and the mean deviation from thenominal speed can be calculated using a linear approximation or, ifnecessary, wavelet approximation to the relevant scale.

FIG. 8D shows the signal after further removal of the linear trend. Atwo-separation harmonic period is clearly shown.

FIG. 8E shows the same signal after the baseline wander is removed usingrobust nonlinear filtering. Here, the repeating shocks are clearly seenevery 4 separations.

FIG. 8F shows composed periods of the signal shown in FIG. 8E. Thisperiod-to-period analysis enhances the repeating patterns. The repeatingpatterns appear in all of the periods, while non-repeating patterns donot appear in all of the periods. The dark, thick line is the median ofthe signals, emphasizing the shocks that represent opening and closingof paper grippers.

Many faults in the Indigo press are manifestations of harmonicperturbations. These perturbations are easily detected by applying aFourier transform to the signal of FIG. 8B (e.g., by signal analyzer106). FIG. 9 shows the Fourier amplitude of the velocity correcteddynamic mirror signal after the baseline removal. A peak at 38.5 Hz isevident, emphasizing the root cause of the fault that can be sensed bydiagnostic module 406.

FIGS. 10, 11 and 12 show methods illustrated as flow diagrams. Forsimplicity of explanation, the methods are depicted and described asseries of acts. However, the methods are not limited by the actsillustrated and by the order of acts. For example, acts can occur invarious orders and/or concurrently, and with other acts not presentedand described herein. Furthermore, not all illustrated acts may berequired to implement the methods. Additionally, it should be furtherappreciated that the methods can be implemented on an article ofmanufacture (e.g., a non-transitory computer-readable storage medium) tofacilitate transporting and transferring the methods. These methods maybe implemented by any suitable system or apparatus, such as described inFIGS. 1-7.

Referring now to FIG. 10, illustrated is a schematic process flowdiagram of a method 1000 for diagnosing errors in a reactive system.Method 1000 can facilitate automatic diagnosis of the root cause ofsystem faults, design flaws of the system, or the like, withoutrequiring an expert.

An expert can focus on the root cause of a fault quickly and accurately,utilizing only a signal or set of signals. The signal or set of signalsanalyzed by the expert are referred to as the “heartbeat” of thereactive system. The “heartbeat” is a signal that reflects most of thecritical health indicators in the reactive system.

At element 1002, a signal (or set of signals) is selected as the“heartbeat” of a reactive system that includes most of the criticalhealth indicators of a fault in the reactive system. At element 1004,the critical health indicators are extracted from the signal. FIGS. 11and 12 illustrate decomposition methods 1100 and 1200 for extracting thecritical health indicators of the system. At element 1006, theindicators are analyzed to facilitate diagnostics of the reactivesystem.

For example, the indicators can be symptoms of a health problem of thesystem. The symptoms can be input into a database that includes varioushealth problems of the system and corresponding symptoms. The symptomscan be matched to a health problem. The health problem can be output(e.g., on a screen or display) along with instructions for fixing theproblem.

Referring now to FIG. 11, illustrated is a schematic process flowdiagram of a method 1100 for decomposing a signal to extract criticalhealth indicators, with the assumption that the critical healthindicators add linearly within the signal. In other words, the heartbeatsignal (or the set of heartbeat signals) is assumed to be adecomposition of basic signals that refer to the critical healthindicators. Since the critical health indicators are assumed to addlinearly, the signal or set of signals can be additively decomposed.

At element 1102, the signal is additively decomposed into the pluralityof indicators. By clever selection of base functions, the decompositioncan be performed in a way such that all fault sources of the system canbe detected through the critical health indicators. To perform thedecomposition, an over complete basis is chosen so that the basefunctions enhance known fault causes. The choice of base functionsenhances the root causes of the faults and facilitates automaticdetection of the root causes.

The base functions can be predefined for different signals fromdifferent reactive systems according to an expert's knowledge. Basefunctions can also be derived from the signal or set of signals. Forexample, base functions can be derived from the signal or set of signalsby applying sparse representation techniques.

At element 1104, based on the decomposed indicators, a root-orienteddiagnostics is performed on the reactive system. The base functions arechosen to enhance the extraction of the critical health indicators. Theroot oriented analysis can be accomplished through an analysis of thecritical health indicators.

Referring now to FIG. 12, illustrated is a schematic process flowdiagram of a method for decomposing a signal to extract critical healthindicators utilizing base functions. At element 1202, a signal isselected that includes the plurality of indicators. At element 1204,base functions are chosen. The base functions can be pre-selected by anexpert or based on the signal itself. The base functions are chosen soto enhance the root cause of the fault. At element 1206, the basefunctions are used to extract the indicators from the signal. At element1208, a root-oriented diagnostics is performed on the reactive systembased on the plurality of indicators.

The above description of illustrated examples, including what isdescribed in the Abstract, is not intended to be exhaustive or to limitthe disclosed examples to the precise forms disclosed. While specificexamples and examples are described herein for illustrative purposes,various modifications are possible that are considered within the scopeof such examples and examples, as those skilled in the relevant art canrecognize.

As used herein, the word “example” is used to mean serving as anexample, instance, or illustration. For the avoidance of doubt, thesubject matter described herein is not limited by such examples. Inaddition, any aspect or design described herein as an “example” is notnecessarily to be construed as preferred or advantageous over otheraspects or designs, nor is it meant to preclude equivalent structuresand techniques known to those of ordinary skill in the art. Furthermore,to the extent that the terms “includes,” “has,” “contains,” and othersimilar words are used in either the detailed description or the claims,such terms are intended to be inclusive—in a manner similar to the term“comprising” as an open transition word—without precluding anyadditional or other elements.

In this regard, while the described subject matter has been described inconnection with various examples and corresponding Figures, whereapplicable, it is to be understood that other similar examples can beused or modifications and additions can be made to the describedexamples for performing the same, similar, alternative, or substitutefunction of the disclosed subject matter without deviating therefrom.Therefore, the disclosed subject matter should not be limited to anysingle example described herein, but rather should be construed inbreadth and scope in accordance with the appended claims.

What is claimed is:
 1. A system, comprising: at least one memory storingcomputer-executable instructions; at least one processor,communicatively coupled to the at least one memory, that facilitatesexecution of the computer-executable instructions to at least: decomposea signal generated by a reactive system to extract a plurality ofindicators of health of the reactive system; and determine a healthstatus of the reactive system based on an analysis of the plurality ofindicators.
 2. The system of claim 1, wherein the at least one processorfurther facilitates execution of the computer-executable instructions tochoose basis functions for the signal with the assumption that thesignal is a linear combination of the plurality of indicators.
 3. Thesystem of claim 1, wherein the at least one processor furtherfacilitates execution of the computer-executable instructions to detecta pattern within the plurality of indicators to indicate a fault.
 4. Thesystem of claim 1, wherein the at least one processor furtherfacilitates execution of the computer-executable instructions todecompose the signal to its basis functions using successive steps, eachof the successive steps comprising an orthogonal projection onto onefamily of basis functions combined with removal of a projected signalcomponent, wherein a projection order is determined by a relativestrength of components of each of the basis functions.
 5. An apparatus,comprising: a signal selector to identify a signal that includes aplurality of known indicators of faulty behavior of the apparatus; asignal analyzer to extract the known indicators from the signal and toperform a self-diagnostic based on the known indicators.
 6. Theapparatus of claim 5, wherein the signal analyzer is configured toperform the self-diagnostic by comparing the known indicators to valuesstored in a database of potential faults of the apparatus.
 7. Theapparatus of claim 5, wherein the signal analyzer is configured toextract the known indicators by decomposing the signal into the knownindicators.
 8. The apparatus of claim 7, wherein the signal is a linearcombination of the known indicators.
 9. The apparatus of claim 5,wherein the signal analyzer is configured to generate serviceinstructions based on the self-diagnostic.
 10. A method, comprising:selecting a signal comprising a plurality of indicators of a fault in areactive system; extracting the plurality of indicators from the signal;and analyzing the plurality of indicators to facilitate diagnostics ofthe reactive system.
 11. The method of claim 10, wherein the extractingfurther comprises decomposing the signal to extract the plurality ofindicators from the signal.
 12. The method of claim 10, wherein theextracting further comprises: assuming that the plurality of indicatorsadd linearly within the signal; and additively decomposing the signalinto the plurality of indicators.
 13. The method of claim 10, whereinthe extracting further comprises: choosing base functions to enhance theplurality of indicators; and utilizing the base functions to extract theplurality of indicators.
 14. The method of claim 10, further comprisingproducing root-cause oriented diagnostics of the reactive system basedon the analyzing the plurality of indicators.
 15. The method of claim10, wherein the analyzing further comprises accessing a database ofpotential faults related to the reactive system and diagnosing a faultof the reactive system by comparing the plurality of indicators toinformation stored in the database of faults.